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From: "Roger T." <roger@indra.com>
Subject: Re: Opinions on Ellipse-Circle dilemma?
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On Fri, 14 Feb 1997, Terry Richards wrote:

> > Because a circle, in every way, meets the definition of an ellipse. That
> > definition is;
> > 
> > x^2/a^2  +  y^2/b^2 = 1
> > 
> > A circle is just a special name for the case of  "a=b".
> 
> Here, I have to disagree. An ellipse can be modified so that a!=b and
> still remain an ellipse. A circle cannot have this operation performed
> on it and still remain a circle. 

That is because the "circle" was never a unique entity that is somehow
distinguishable as different from an ellipse. If you dispense with the
need to classify a circle as seperate from an ellipse then you seen that
the shape was, is, and always will be an ellipse. Whenever the a & b
params are equal the ellipse can be described as being in the "circle
state". To simplify that description we refer to that ellipse as a
circle. But in fact it is still an ellipse. 


> I agree that an ellipse with a=b is
> mathamatically indistinguishable from the equivalent circle *at that
> time*. However, the ellipse still has properties that the circle does
> not have in that it can change in ways that the circle cannot.

Your problem is you continue to insist that a circle is a unique type of
entity that is somehow not covered by the definition of ellipse. That is
not the case.

To illustrate: 

Would you identify "Joe in the kitchen" as being a uniquely classifiable
abstraction in comparison to "Joe in the den"? No you wouldn't. You would
simply create the "Joe" abstraction and add a location parameter so that
you could cover both the description of "Joe in the kitchen" and "Joe in
the den".

Roger T.



